Ju n 20 23 A review of the geometrical thermodynamics and its application to black holes

This paper presents a comprehensive review of geometrical thermodynamics, which employs geometric concepts to study the thermodynamic properties of physical systems. The review covers key topics such as thermodynamic fluctuation theory, proposed thermodynamic metrics in various coordinate systems, and thermodynamic curvature. Additionally, the paper discusses the geometrical approach to black hole thermodynamics and provides an overview of recent research in this field.

[1]  D. Raine.  General relativity , 1980, Nature.

[2]  Yong-qiang Wang,et al.  Dynamic properties of thermodynamic phase transition for five-dimensional neutral Gauss-Bonnet AdS black hole on free energy landscape , 2020, Nuclear Physics B.

[3]  R. Mann,et al.  Thermodynamics of de Sitter black holes with conformally coupled scalar fields , 2020, Journal of High Energy Physics.

[4]  R. Mann,et al.  Reverse Hawking-Page phase transition in de Sitter black holes , 2018, Journal of High Energy Physics.

[5]  Maureen T. Carroll.  Geometry , 2017, MAlkahtani Mathematics.

[6]  M. D. Le'on,et al.  A geometric approach to solve time dependent and dissipative Hamiltonian systems , 2016, 1607.01239.

[7]  H. Quevedo,et al.  Ideal quantum gases: A geometrothermodynamic approach , 2015, Journal of Geometry and Physics.

[8]  J. W. Cannon.  Connecting thermodynamics to students’ calculus , 2004 .

[9]  A. Banyaga.  The Structure of Classical Diffeomorphism Groups , 1997 .

[10]  H. Callen.  Thermodynamics and an Introduction to Thermostatistics , 1988 .

[11]  W. L. Burke.  Applied Differential Geometry , 1985 .

[12]  P. Salamon,et al.  Geometry of the ideal gas. , 1985, Physical review. A, General physics.

[13]  James W. Bawden,et al.  Transitions , 1984 .

[14]  Brandon Carter,et al.  The four laws of black hole mechanics , 1973 .

[15]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[16]  Chien-Chung Cheng.  Maxwell's Equations in Dynamics , 1966 .

[17]  D. Laugwitz.  Differential and Riemannian Geometry , 1966 .

[18]  R. Dedekind,et al.  Gesammelte mathematische Werke , 1932 .

[19]  C. Barus.  AN AMERICAN JOURNAL OF PHYSICS. , 1902, Science.

[20]  H. Janyszek,et al.  Curvature of the Weinhold Metric for Thermodynamical Systems with 2 Degrees of Freedom , 2018 .

[21]  P. Mazur.  BLACK HOLE UNIQUENESS THEOREMS , 2008 .

[22]  P. Murdin.  MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY , 2005 .

[23]  R. Adamson.  Black holes and thermodynamics , 2003 .

[24]  Jean-Baptiste Lully,et al.  The collected works , 1996 .

[25]  L. Beda.  Thermal physics , 1994 .